Light sources of high luminance are used in greatly varying fields, in endoscopy and also in projection devices. The most recent developments relate in this case to the combination of a pump light source of high power density, for example, a laser, with a phosphor element which converts pump light, and which is arranged spaced apart from the pump light source. A conversion of ultraviolet or blue pump light, for example, into converted light of longer wavelength occurs by way of the phosphor element, specifically a phosphor provided on a carrier in layer form.